Green’s Dictionary of Slang

(US) a telling advantage, e.g. a hidden weapon.

1903		T.W. Jackson Slow Train 70: ‘Yo’ is twice as big as him.’ ‘Yes, but Charlie carries de diffunce ’round in his pocket.’.
1938		W. Pegler in Nevada State Journal (Reno) 21 Dec. 6/2: A gun was also known as the difference [...] denoting the margin of power and courage between the man who had one and the man unarmed.
1947		N. Algren Neon Wilderness (1986) 219: Even if a guy got the difference on him he don’t want to get too close to no man with broken glass in his hand.
1956		‘James Updyke’ [W.R. Burnett] It’s Always Four O’Clock 70: Walt also ended up almost getting shot because this Texas boy was real rough and sometimes packed the difference.
1975		E. Torres Carlito’s Way 18: He pulls out the difference, size .38.